The discriminatory incentives to bundle in the cable television industry

Abstract

An influential theoretical literature supports a discriminatory explanation for product bundling: it reduces consumer heterogeneity, extracting surplus in a manner similar to second-degree price discrimination. This paper tests this theory and quantifies its importance in the cable television industry. The results provide qualified support for the theory. While bundling of general-interest cable networks is estimated to have no discriminatory effect, bundling an average top-15 special-interest cable network significantly increases the estimated elasticity of cable demand. Calibrating these results to a simple model of bundle demand with normally distributed tastes suggests that such bundling yields a heterogeneity reduction equal to a 4.7% increase in firm profits (and 4.0% reduction in consumers surplus). The results are robust to alternative explanations for bundling.

Keywords

Bundling Price discrimination Cable television

We are grateful to the editor and two anonymous referees for their detailed comments on the paper. We would also like to thank Cathleen McHugh for her assistance inputting the data, Mike Riordan, Joe Harrington, Matt Shum, Steve Coate, Roger Noll, Bruce Owen, V. Kerry Smith, Mark Coppejans, Frank Wolak, Phillip Leslie, and seminar participants at Cornell University and the 1999 IDEI/NBER Econometrics of Price and Product Competition conference for helpful comments.

JEL Classification

Appendix

Appendix 1: Proofs of propositions

Suppose there are n discrete products (components) supplied by a monopolist and consumers differ in their preferences (willingness-to-pay) for each of these products, given by a type vector, vi = (vi1, ..., vin). Let each vic, c = 1, ..., n, be independent with means μc and variances σc. Let \(x_{in} \equiv \frac{1}{n} \sum_{c=1}^{n} v_{ic}\) be the per-good valuation for consumer i of a bundle of n goods, let μn be its mean, and let \(\sigma^2_n\) be its variance. Note that μn and \(\sigma^2_n\) follow the well-known formulas for the mean and variance of an average of (independent) random variables:

Case II Aggregate bundle elasticity. When considering the impact of increases in n on the aggregate bundle elasticity, one has to accommodate that a given change in the per-good bundle price has a larger effect on the aggregate price for a larger bundle than for a smaller bundle. While this does not impact the elasticity of the size-n bundle demand curve evaluated at price pn, it does impact the elasticity of the size-(n + 1) bundle demand curve evaluated at price pn. In particular,

Under A4, it is easy to show that for the per-good elasticities, \(\epsilon^{n+1}(p_n) \geq \epsilon^{n}(p_n)\). For the aggregate size-(n + 1) bundle elasticity, however, we must scale \(\epsilon^{n+1}(p_n)\) by A(n) < 1. What impact does this have on the comparison? One can show that \(\tilde{\epsilon}^{n+1}(\tilde{p}_n) \geq \tilde{\epsilon}^{n}(\tilde{p}_n)\) whenever the right-hand side of the last inequality in Eq. 8 is greater than the right-hand side of the last inequality in Eq. 6. This holds for all n.47

Proof of Proposition 2

Let preferences be as for Proposition 1 above except in allowing for correlation between consumer valuations, vi = (vi1, ..., vin). Let ρc,d = corr(vic,vid). With correlation, the variance of the per-good valuation for a bundle of size n, xin, may be written as

The primary benefit of bundling is due to heterogeneity reduction as measured by the variance of per-good tastes for the bundle, \(\sigma^2_n\). Unlike for Proposition 1 above, once we allow for correlation in tastes, bundle size, n, is not a sufficient statistic for \(\sigma^2_n\). In particular, adding a new good to a bundle changes \(\sigma^2_n\) by both (1) changing \(\bar{\sigma}^2_c\) and (2) increasing n.

This is a more general statement of Eq. 7 above.48 Reducing the (limiting) variance of the bundle (e.g. by increasing n or reducing σ2) makes per-good demand for a bundle of size n more elastic.

The result of the proposition follows from Eq. 11. To see this, suppose the bundle had only two goods (i.e. component 2 was the nth good). It is easy to see that \(\frac{\partial \sigma^2_n}{\partial \rho_{1,2}} > 0\), i.e. making the correlation between components 1 and 2 more negative reduces \(\sigma^2_n\). Since, \(\frac{\partial \eta}{\partial \sigma^2} >0\) it follows that \(\frac{\partial \epsilon^{n}}{\partial \rho_{\tilde{1},2}} < 0\): making correlations more negative makes the bundle demand curve more elastic. For the case of general n, simply note that the variance of a bundle of size n can be decomposed into the variance of a bundle of size (n − 1), the variance of component n, and twice the covariance between a bundle of size (n − 1) and component n.

Appendix 2: Instruments

In this appendix, we present an analysis of the instruments used for prices and network carriage in the econometric analysis.

Price instruments To assess the power of the price instruments, Table 7 presents results from reduced form regressions of prices on the instruments and exogenous variables.49 The results are organized in sets of three columns. For each set of three, the first column reports the point estimates from the regression of the price of basic service, pb, on the instruments and included exogenous variables. Similarly in the second and third columns for the price of Expanded basic services I and II, pI and pII, if offered.

Table 7

First-stage estimation, prices

Price inst: Cost

Price inst: MSO prices

Instrument

Dependent variable

Instrument

Dependent variable

pb

pI

pII

pb

pI

pII

Homes passed, basic

0.00

0.00

0.00

IPB

0.64

0.03

0.13

(0.03)

(0.01)

(0.01)

(0.07)

(0.10)

(0.20)

MSO subs, basic

0.01

0.00

−0.03

IPE

−0.03

0.34

−0.17

(0.01)

(0.01)

(0.02)

(0.12)

(0.13)

(0.31)

MSO subs2, basic

0.00

0.00

0.00

IPF

−0.22

0.48

−0.41

(0.00)

(0.00)

(0.00)

(0.24)

(0.42)

(0.42)

Affiliation, basic

−3.48

0.96

0.36

(1.22)

(2.13)

(1.48)

Channel capacity, basic

0.03

0.02

0.00

(0.08)

(0.02)

(0.00)

Homes passed, expanded I

−0.02

–

–

(0.03)

MSO subs, expanded I

0.00

–

–

(0.01)

MSO subs2, expanded I

0.00

–

–

(0.00)

Affiliation, expanded I

6.12

–

–

(3.83)

Channel capacity, expanded I

−0.05

–

–

(0.02)

Homes passed, expanded II

0.01

−0.01

–

(0.01)

(0.01)

MSO subs, expanded II

0.06

−0.04

–

(0.03)

(0.04)

MSO subs2, expanded II

0.00

0.00

–

(0.00)

(0.00)

Affiliation, expanded II

−8.63

−1.54

–

(4.32)

(2.27)

Channel capacity, expanded II

0.00

−0.01

–

(0.03)

(0.03)

Observations

1,159

429

168

Observations

1,159

429

168

R-squared

0.649

0.818

0.888

R-square

0.720

0.818

0.888

p value

0.000

0.567

0.000

p value

0.000

0.029

0.350

Reported are results from reduced form estimation of prices for basic service (b) and up to two expanded basic services (I, II), on the instruments and exogenous variables. Results are organized in sets of three columns. The first set report estimates using Cost shifters as instruments, defined as homes passed, number and square of subscribers served by same firm (MSO), owner affiliation with programming networks, and channel capacity, interacted with cable service dummy variables. Separate effects for each service are not identified for some parameters in the Expanded Service equations. The second set of columns report estimates using MSO Prices as instruments, defined for each service as the average price for that service at other systems owned by the same MSO. Reported p value in each column is for hypothesis test of joint insignificance of reported parameters.

The first set of three columns report estimates using cost shifters as instruments for cable prices. As these shifters do not vary across services, we interact them with cable service dummy variables to allow their effects to differ by service. Reported are the estimated parameters for these interactions.50 Evidence in support of the cost instruments is mixed. While homes passed does not appear to be an important cost shifter in any equation, the remaining variables enter intermittently. Most influential are affiliation (negative and significant in the first and third columns) and MSO subscribers and its square (negative for large values and occasionally significant in the first and third columns). Channel capacity enters as expected only in the second column. That said, p values associated with the hypothesis test of joint insignificance for all parameters are trivially small in all but the expanded I equation.51 On balance, while supporting their use as instruments, lack of variation across services and an indirect connection to marginal costs suggests the cost shifters may be weak instruments.

The second set of three columns report estimates using prices of cable services of other systems within an MSO as instruments.52 The results are quite promising. Other-system prices within an MSO provide strong and significant effects for both basic and Expanded I equations, particularly for prices of the same service. Results for a second expanded service are poor, possibly due to relatively few observations. As expected, p values associated with the hypothesis of joint insignificance are soundly rejected for the basic and Expanded I equations.

Network instruments To assess the power of the network instruments, Table 8 presents a synopsis of reduced form (probit) regressions of network carriage on the instruments and included exogenous variables. As above, the results are organized in sets of three columns. As we must predict the carriage of each of the top-15 cable networks (as well as the sum of other cable networks) on all the exogenous variables and instruments, the number of estimations performed was considerable.53 Rather than report the point estimates of the instruments for each specification, we simply report the p value from the hypothesis test of joint insignificance of the instrument set. As can be seen from the table, the instruments have considerable power, at least for the basic and first expanded basic equation.54 Coefficient estimates were as expected—particularly powerful predictors of the carriage of network q on service s was the corresponding likelihood it was carried on service s by other systems within its MSO.

Table 8

First-stage estimation, network carriage

Instrument

Dependent Variable

\(\mbox{NET}_b\)

\(\mbox{NET}_{I}\)

\(\mbox{NET}_{II}\)

WTBS

<0.001

<0.001

0.002

Discovery

<0.001

<0.001

0.240

ESPN

<0.001

0.029

0.249

USA

<0.001

0.020

0.082

CSPAN

<0.001

0.229

–

TNT

<0.001

<0.001

0.065

Family

<0.001

<0.001

0.701

Nashville

<0.001

0.001

0.222

Lifetime

<0.001

<0.001

–

CNN

<0.001

<0.001

–

A&E

<0.001

0.016

–

Weather

<0.001

<0.001

0.067

QVC

<0.001

0.089

–

Learning

<0.001

0.084

–

MTV

<0.001

0.011

–

Other Satellite

<0.001

<0.001

<0.001

Observations

1,159

429

168

Reported are results of reduced form (probit) estimation of the carriage of each reported network on Basic Service (b) and up to two expanded basic services (I, II), on the instruments and exogenous variables. All specifications use MSO Networks as network instruments, defined for each network on each service as the proportion of other systems owned by the same MSO carrying that network on that service. Reported are p values for hypothesis test of joint insignificance of network instruments. Lack of carriage on Expanded Service II prevented identification of the impact of instruments for some networks.